Is the son of the sister by breastfeeding considered a mahram in Islam, and is it permissible for a woman to go for Hajj with him?
Everything that is prohibited by lineage is also prohibited by breastfeeding. The son of the sister by breastfeeding is considered a mahram, just like the son of the sister by blood, and it is permissible for him to be her mahram for Hajj and Umrah. And Allah Knows Best.
Is it permissible for the person who hasn`t made wudu` (state of minor ritual impurity) to perform the Adhan?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
It is disliked (Makruh) for a person in a state of minor ritual impurity (Hadath Asghar) to perform the Adhan. However, if he does so, his Adhan is considered valid and fulfills the sunnah of the Adhan despite it being disliked. And Allah the Exalted knows best.
What is the ruling on having an intention (Niyyah) for every prayer?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
Intention (Niyyah) is a pillar (Rukn) without which the prayer is not valid. The worshiper must have an intention for every prayer, meaning they must consciously intend the act of worship they are performing. Its timing must coincide with the opening Takbir (Takbirat al-Ihram). It is not a requirement to utter it verbally; rather, doing so is considered a recommended Sunnah. There are three levels of intention:
1-If the prayer is obligatory (Fard): It is mandatory to include the Intent (to pray), the Specification (which prayer, e.g., 'Asr), and the Obligation (recognizing it as a Fard). For example, one should bring to mind or say: 'I intend to pray the Fard of 'Asr.'
2-If it is a voluntary prayer restricted by a specific time or cause (Sunnah Muqayyadah): It is mandatory to include the Intent and the Specification. For example: 'I intend to pray the Sunnah before Zuhr' or 'I intend to pray Duha.'
3-If it is an absolute voluntary prayer (Nafl Mutlaq): It is sufficient to simply have the Intent to pray. For example: 'I intend to pray.'
And Allah the Exalted knows best.
Is fasting obligatory for a child?
Fasting is not obligatory for a child until they reach puberty. Puberty is determined by well-known signs, the most common of which are: nocturnal emission (for both males and females), menstruation (for females), or reaching the age of fifteen lunar years.
A guardian must instruct their children to fast once they reach the age of discernment, which is around seven years old, if they are capable of fasting.